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View File - University of Engineering and Technology, Taxila

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Zero Forcing Technique. Suppose the output <strong>of</strong> the equalizer z eq ðtÞ inresponse to the channel output z c ðtÞ can be written asz eq ðtÞ ¼ PNn¼a n z c ðt nTÞ ð3:29ÞNassuming that the tap spacing corresponds to the time T the equalizer issampled. Our objective is for the equalizer output z eq ðtÞ to satisfy Nyquist’spulse-shaping criterion. So if we set t ¼ mT, we can rewrite (3.29) asz eq ðmTÞ ¼ PNn¼Na n z c ½ðm nÞTŠ ¼ 1; m ¼ 00; m 6¼ 0ð3:30Þwhere m ¼ 0; 1; 2; 3; ...; N. Since 2N þ 1 coefficients will beselected from (3.30), it therefore follows that Nyquist’s criterion can besatisfied at only 2N þ 1 time instants. If we can write the equalizer output,the tap weights, <strong>and</strong> channel output in matrix format, Eq. (3.30) can be writtenin the form½z eq Š¼½hŠ½z c Šð3:31Þwhere2 300..0½z eq Š¼1006.74 . 50ð3:32aÞCopyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.

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